Nonlinear Ill-posed Problems of Monotone Type

Nonlinear Ill-posed Problems of Monotone Type
Author: Yakov Alber
Publisher: Springer Science & Business Media
Total Pages: 422
Release: 2006-02-23
Genre: Mathematics
ISBN: 1402043961

Interest in regularization methods for ill-posed nonlinear operator equations and variational inequalities of monotone type in Hilbert and Banach spaces has grown rapidly over recent years. Results in the field over the last three decades, previously only available in journal articles, are comprehensively explored with particular attention given to applications of regularization methods as well as to practical methods used in computational analysis.

Theory and Applications of Nonlinear Operators of Accretive and Monotone Type

Theory and Applications of Nonlinear Operators of Accretive and Monotone Type
Author: Athanass Kartsatos
Publisher: CRC Press
Total Pages: 338
Release: 1996-03-14
Genre: Mathematics
ISBN: 9780824797218

This work is based upon a Special Session on the Theory and Applications of Nonlinear Operators of Accretive and Monotone Type held during the recent meeting of the American Mathematical Society in San Francisco. It examines current developments in non-linear analysis, emphasizing accretive and monotone operator theory. The book presents a major survey/research article on partial functional differential equations with delay and an important survey/research article on approximation solvability.

Nonlinear Ill-posed Problems of Monotone Type

Nonlinear Ill-posed Problems of Monotone Type
Author: Yakov Alber
Publisher: Springer
Total Pages: 410
Release: 2009-09-03
Genre: Mathematics
ISBN: 9789048107209

Interest in regularization methods for ill-posed nonlinear operator equations and variational inequalities of monotone type in Hilbert and Banach spaces has grown rapidly over recent years. Results in the field over the last three decades, previously only available in journal articles, are comprehensively explored with particular attention given to applications of regularization methods as well as to practical methods used in computational analysis.

Nonlinear Ill-posed Problems of Monotone Type

Nonlinear Ill-posed Problems of Monotone Type
Author: Yakov Alber
Publisher: Springer Science & Business Media
Total Pages: 432
Release: 2006-02-02
Genre: Mathematics
ISBN: 9781402043956

Interest in regularization methods for ill-posed nonlinear operator equations and variational inequalities of monotone type in Hilbert and Banach spaces has grown rapidly over recent years. Results in the field over the last three decades, previously only available in journal articles, are comprehensively explored with particular attention given to applications of regularization methods as well as to practical methods used in computational analysis.

Regularization Algorithms for Ill-Posed Problems

Regularization Algorithms for Ill-Posed Problems
Author: Anatoly B. Bakushinsky
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 342
Release: 2018-02-05
Genre: Mathematics
ISBN: 3110557355

This specialized and authoritative book contains an overview of modern approaches to constructing approximations to solutions of ill-posed operator equations, both linear and nonlinear. These approximation schemes form a basis for implementable numerical algorithms for the stable solution of operator equations arising in contemporary mathematical modeling, and in particular when solving inverse problems of mathematical physics. The book presents in detail stable solution methods for ill-posed problems using the methodology of iterative regularization of classical iterative schemes and the techniques of finite dimensional and finite difference approximations of the problems under study. Special attention is paid to ill-posed Cauchy problems for linear operator differential equations and to ill-posed variational inequalities and optimization problems. The readers are expected to have basic knowledge in functional analysis and differential equations. The book will be of interest to applied mathematicians and specialists in mathematical modeling and inverse problems, and also to advanced students in these fields. Contents Introduction Regularization Methods For Linear Equations Finite Difference Methods Iterative Regularization Methods Finite-Dimensional Iterative Processes Variational Inequalities and Optimization Problems

Iterative Methods for Ill-posed Problems

Iterative Methods for Ill-posed Problems
Author: Anatoly B. Bakushinsky
Publisher: Walter de Gruyter
Total Pages: 153
Release: 2011
Genre: Mathematics
ISBN: 3110250640

Ill-posed problems are encountered in countless areas of real world science and technology. A variety of processes in science and engineering is commonly modeled by algebraic, differential, integral and other equations. In a more difficult case, it can be systems of equations combined with the associated initial and boundary conditions. Frequently, the study of applied optimization problems is also reduced to solving the corresponding equations. These equations, encountered both in theoretical and applied areas, may naturally be classified as operator equations. The current textbook will focus on iterative methods for operator equations in Hilbert spaces.

Inverse Problems

Inverse Problems
Author: Alexander G. Ramm
Publisher: Springer Science & Business Media
Total Pages: 453
Release: 2005-12-19
Genre: Technology & Engineering
ISBN: 0387232184

Inverse Problems is a monograph which contains a self-contained presentation of the theory of several major inverse problems and the closely related results from the theory of ill-posed problems. The book is aimed at a large audience which include graduate students and researchers in mathematical, physical, and engineering sciences and in the area of numerical analysis.

Variational Methods in Nonlinear Analysis

Variational Methods in Nonlinear Analysis
Author: Dimitrios C. Kravvaritis
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 499
Release: 2020-04-06
Genre: Mathematics
ISBN: 3110647389

This well-thought-out book covers the fundamentals of nonlinear analysis, with a particular focus on variational methods and their applications. Starting from preliminaries in functional analysis, it expands in several directions such as Banach spaces, fixed point theory, nonsmooth analysis, minimax theory, variational calculus and inequalities, critical point theory, monotone, maximal monotone and pseudomonotone operators, and evolution problems.

Geometric Properties of Banach Spaces and Nonlinear Iterations

Geometric Properties of Banach Spaces and Nonlinear Iterations
Author: Charles Chidume
Publisher: Springer
Total Pages: 337
Release: 2008-12-21
Genre: Mathematics
ISBN: 1848821905

The contents of this monograph fall within the general area of nonlinear functional analysis and applications. We focus on an important topic within this area: geometric properties of Banach spaces and nonlinear iterations, a topic of intensive research e?orts, especially within the past 30 years, or so. In this theory, some geometric properties of Banach spaces play a crucial role. In the ?rst part of the monograph, we expose these geometric properties most of which are well known. As is well known, among all in?nite dim- sional Banach spaces, Hilbert spaces have the nicest geometric properties. The availability of the inner product, the fact that the proximity map or nearest point map of a real Hilbert space H onto a closed convex subset K of H is Lipschitzian with constant 1, and the following two identities 2 2 2 ||x+y|| =||x|| +2 x,y +||y|| , (?) 2 2 2 2 ||?x+(1??)y|| = ?||x|| +(1??)||y|| ??(1??)||x?y|| , (??) which hold for all x,y? H, are some of the geometric properties that char- terize inner product spaces and also make certain problems posed in Hilbert spaces more manageable than those in general Banach spaces. However, as has been rightly observed by M. Hazewinkel, “... many, and probably most, mathematical objects and models do not naturally live in Hilbert spaces”. Consequently,toextendsomeoftheHilbertspacetechniquestomoregeneral Banach spaces, analogues of the identities (?) and (??) have to be developed.

Recovery Methodologies: Regularization and Sampling

Recovery Methodologies: Regularization and Sampling
Author: Willi Freeden
Publisher: American Mathematical Society
Total Pages: 505
Release: 2023-08-21
Genre: Mathematics
ISBN: 1470473453

The goal of this book is to introduce the reader to methodologies in recovery problems for objects, such as functions and signals, from partial or indirect information. The recovery of objects from a set of data demands key solvers of inverse and sampling problems. Until recently, connections between the mathematical areas of inverse problems and sampling were rather tenuous. However, advances in several areas of mathematical research have revealed deep common threads between them, which proves that there is a serious need for a unifying description of the underlying mathematical ideas and concepts. Freeden and Nashed present an integrated approach to resolution methodologies from the perspective of both these areas. Researchers in sampling theory will benefit from learning about inverse problems and regularization methods, while specialists in inverse problems will gain a better understanding of the point of view of sampling concepts. This book requires some basic knowledge of functional analysis, Fourier theory, geometric number theory, constructive approximation, and special function theory. By avoiding extreme technicalities and elaborate proof techniques, it is an accessible resource for students and researchers not only from applied mathematics, but also from all branches of engineering and science.